Flop odds, not hand odds

if this question is posted and answered here already, I apologize, I couldn't locate it.

in texas hold 'em what are the odds of the flop being 3 of a kind? how often should this happen? (statistics) How many hands should it take? I found different numbers on different sites, I would like to see the math. thanks

I'm not talking about anything to do with my hand. My quetion is how many hands should it take to see the flop come as 777 or KKK? Not hand odds of trips or quads, JUST the flop only being 3OAK

Quote: strikeu

if this question is posted and answered here already, I apologize, I couldn't locate it.

in texas hold 'em what are the odds of the flop being 3 of a kind? how often should this happen? (statistics) How many hands should it take? I found different numbers on different sites, I would like to see the math. thanks

I'm not talking about anything to do with my hand. My quetion is how many hands should it take to see the flop come as 777 or KKK? Not hand odds of trips or quads, JUST the flop only being 3OAK

Not too hard ...

There are combin(52,3) = 22,100 different flops.

There are 4 flops of any given rank that are trips. There are 13 ranks. So there are 52 total flops that can be trips.

So the probability of trips on the flop is: 52/22100 = 0.0023529 (more or less).

The frequency is 1/p = 22100/52 = 425.

So, once every 425 flops you'll see trips.

The odds are 424-to-1.

would you need to take into account the number of people playing? ie the number of cards dealt or burned preflop?

Quote: strikeu

would you need to take into account the number of people playing? ie the number of cards dealt or burned preflop?

None of that matters as long as you know there's going to be a flop every single hand. Seen and unseen cards are irrelevant if the flop is guaranteed.

However, if sometimes there is no flop, then there is a selection taking place on the remaining cards over which the flops are being determined. Thus the odds of trips are dependent on the hands players play, which makes the problem essentially unsolvable. For example, if players fold every hand (even the blinds) except those holding an ace, then trip aces are impossible. Why? No flop is seen unless each calling player holds an ace. There are at least two players, ergo, no trip aces. If players play only hands with an ace or a pair, there is a similar problem. In this case you are asking for the frequency of trips over "seen" flops. That's a flop of a different color.

If you take the poker playing out of it, it's the exact same odds as getting 3OAK in 3 Card Poker. 52 cards, 3OAK with 3 cards is always .0024.